I've noticed there's been an increase in discussions about IPv6 across some forums. Should I start thinking about upgrading to IPv6?
You've already had a lot of well considered answers. I wanted to take issue with your use of the term "upgrading". IPv6 is simply a alternative layer 3 protocol to IPv4; it's not inherently better, though it aims to address some of the deficiencies of IPv4, especially the small and essentially exhausted address space. The experience of watching a YouTube video is the same whether the traffic comes over IPv6 or IPv4.
Without deliberate steps to provide interworking that are not generally applicable, IPv6 and IPv4 do not interconnect, so you cannot access an IPv4 server from an IPv6 host and vice versa. This is not currently a significant issue for general Internet use, as there are only a handful of servers that a typical UK Internet user would encounter that are IPv6 only - mostly services that have been deliberately provisioned as IPv6 only such as RevK's Loops Of Zen
(which is currently responding to me over IPv6 with a HTTP 403 forbidden error). However, as we get deeper into IPv4 exhaustion, there will be an increasing number of scenarios that cannot be handled with IPv4 - in particular endpoints served using CG NAT cannot accept any inbound connections. If you need to access a corporate VPN server or mail server that is IPv6 only, you need IPv6 connectivity.
At the moment, IPv6 is more a concern for server operators, who should be working towards ensuring all their services are on the IPv6 Internet if they are not already there. It will become increasingly common for end users to have no IPv4 connectivity, though this is not likely for those using a UK consumer Internet connection in the near future. IPv6 support differs amongst the major companies; Google and Facebook have strong IPv6 support whereas Amazon still has a way to go (especially with AWS).
I would argue that the time has arrived when consumer Internet access should include IPv6, not least as a recognition that IPv6 support in consumer laptops, tablets and phones is now mature and IPv6 will be the future of the Internet. Indeed, many networked printers now have good quality IPv6 support. The only way to start eliminating the huge technical debt connected with IPv4 is to transition to IPv6. Unfortunately, there is a huge population of IPv4 only devices that are still useful - many if not most of the connected devices you can buy today, other than computers, tablets and phones, are still IPv4 only.
Unless you have a pressing need for IPv6 connectivity today, such as developing and testing software that must work with IPv6 Internet endpoints, it is not essential to have IPv6 today. However, it is worth deploying IPv6 when you can. Make sure you know how to turn IPv6 off on your router in case you hit problems when IPv6 is on.